Sensorless Self-Excited Vibrational Viscometer with Two Hopf Bifurcations Based on a Piezoelectric Device

Abstract

In this study, we propose a high-sensitivity sensorless viscometer based on a piezoelectric device. Viscosity is an essential parameter frequently used in many fields. The vibration type viscometer based on self-excited oscillation generally requires displacement sensor although they can measure high viscosity without deterioration of sensitivity. The proposed viscometer utilizes the sensorless self-excited oscillation without any detection of the displacement of the cantilever, which uses the interaction between the mechanical dynamics of the cantilever and the electrical dynamics of the piezoelectric device attached to the cantilever. Since the proposed viscometer has fourth-order dynamics and two coupled oscillator systems, the systems can produce different self-excited oscillations through different Hopf bifurcations. We theoretically showed that the response frequency jumps at the two Hopf bifurcation points and this distance between them depends on the viscosity. Using this distance makes measurement highly sensitive and easier because the jump in the response frequency can be easily detected. We experimentally demonstrate the efficiency of the proposed sensorless viscometer by a macro-scale measurement system. The results show the sensitivity of the proposed method is higher than that of the previous method based on self-excited oscillation with a displacement sensor.

Measuring Viscosity Using the Hysteresis of the Non-Linear Response of a Self-Excited Cantilever

“…Furthermore, it was observed that the position of the jumps from low to high frequencies (increasing R 2 ) and from high to low frequencies (decreasing R 2 ) did not match. This defined an hysteresis region delimited by two bifurcations, as also found in [ 27 ].…”

“…Constant values of the potentiometer R 1 ( R 1 = 6.11 kΩ) and polarity ( p = −1 with P = 1) were chosen so that sudden jumps in oscillation frequency were observed when sweeping R 2 [ 24 , 27 ].…”

“…Recent works described in [ 26 , 27 ] also report the presence of sudden jumps of the oscillation frequencies of self-excited resonators, but showing, in addition, a hysteresis region in the position of these jumps. To study the hysteresis region in [ 27 ], the authors develop a self-excited (macro)cantilever by coupling the mechanical dynamics of the cantilever with the electrical dynamics of the piezoelectric layer attached to the cantilever and responsible for its excitation (hence, avoiding using an external displacement detector). They analytically analyzed the fourth-order dynamics of the full system and showed the existence of two Hopf bifurcations by studying the root locus of the eigenvalues of the system.…”

Photothermal Self-Excitation of a Phase-Controlled Microcantilever for Viscosity or Viscoelasticity Sensing

“…These limitations can be mitigated by inducing the self-oscillation of the resonator in closed-loop feedback platforms, with a better signal-to-noise ratio and quality factor. The problem with these strategies is that they tend to be very non-linear and difficult to model and analyse [ 22 , 23 , 24 , 25 , 26 ]. The use of a Phase-Locked Loop (PLL) to detect low-noise and real-time shifts of frequency caused by changes in the viscosity of the fluid has recently been successfully proposed [ 27 ].…”

Design of active network filters as hysteretic sensors

“…A design problem of a similar qualitative nature is that envisioned in [18] of a network of piezoelectric ultrasonic active sensors embedded throughout a structure and powered by harvested vibrational energy from the structure. In [24], self-excitability and parameter hysteresis are leveraged to develop a vibrational viscometer with improved performance relative to traditional sensor designs relying on frequency-response analysis. Coupling between a physical micro-cantilever and a virtual cantilever simulated by an analog circuit is used in [12] to achieve high-sensitivity mass measurements of tens of nanograms.…”